Undercover Economist

We don’t have a good sense of our own fallibility. Checking my answers, it was the one I felt the most certain of that I got wrong

In 1913 Robert Millikan published the results of one of the most famous experiments in the history of physics: the “oil drop” experiment that revealed both the electric charge on an electron and, indirectly, the mass of the electron too. The experiment led in part to a Nobel Prize for Millikan but it is simple enough for a school kid to carry it out. I was one of countless thousands who did just that as a child, although I found it hard to get my answers quite as neat as Millikan’s.

We now know that even Millikan didn’t get his answers quite as neat as he claimed he did. He systematically omitted observations that didn’t suit him, and lied about those omissions. Historians of science argue about the seriousness of this cherry-picking, ethically and practically. What seems clear is that if the scientific world had seen all of Millikan’s results, it would have had less confidence that his answer was right.

This would have been no bad thing, because Millikan’s answer was too low. The error wasn’t huge — about 0.6 per cent — but it was vast relative to his stated confidence in the result. (For the technically minded, Millikan’s answer is several standard deviations away from modern estimates: that’s plenty big enough.)

There is a lesson here for all of us about overconfidence. Think for a moment: how old was President Kennedy when he was assassinated? How high is the summit of Mount Kilimanjaro? What was the average speed of the winner of last year’s Monaco F1 Grand Prix? Most people do not know the exact answers to these questions but we can all take a guess.

Let me take a guess myself. JFK was a young president but I’m pretty sure he was over 40 when elected. I’m going to say that when he died he was older than 40 but younger than 60. I climbed Kilimanjaro many years ago and I remember it being 6,090-ish metres high. Let’s say, more than 6,000m but less than 6,300m. As for the racing cars, I think they can do a couple of hundred miles an hour but I know that Monaco is a slow and twisty track. I’ll estimate that the average speed was above 80mph but below 150mph.

Psychologists have conducted experiments asking people to answer such questions with upper and lower bounds for their answers. We don’t do very well. Asked to produce wide margins of error, such that 98 per cent of answers fall within that margin, people usually miss the target 20-40 per cent of the time; asked to produce a tighter margin, such that half the answers are correct, people miss the target two-thirds of the time.

We don’t have a good sense of our own fallibility. Despite the fact that I am well aware of such research, when I went back to check my own answers, it was the one I felt most certain of that I got wrong: Kilimanjaro is just 5,895m high. It seemed bigger at the time.

But there’s another issue here. The charismatic Nobel laureate Richard Feynman pointed out in the early 1970s that the process of fixing Millikan’s error with better measurements was a strange one: “One is a little bit bigger than Millikan’s, and the next one’s a little bit bigger than that, and the next one’s a little bit bigger than that, until finally they settle down to a number which is higher. Why didn’t they discover the new number was higher right away?”

What was probably happening was that whenever a number was close to Millikan’s, it was accepted without too much scrutiny. When a number seemed off it would be viewed with scepticism and reasons would be found to discard it. And since Millikan’s estimate was too low, those suspect measurements would typically be larger than Millikan’s. Accepting them was a long and gradual process.

Feynman added that scientists have learnt their lesson and don’t make such mistakes any more. Perhaps that’s true, although a paper published by the decision scientists Max Henrion and Baruch Fischhoff, almost 15 years after Feynman’s lecture, found that same pattern of gradual convergence in other estimates of physical constants such as Avogadro’s number and Planck’s constant. From the perspective of the 1980s, convergence continued throughout the 1950s and 1960s and sometimes into the 1970s.

Perhaps that drift continues today even in physics. Surely it continues in messier fields of academic inquiry such as medicine, psychology and economics. The lessons seem clear enough. First, to be open to ourselves and to others about the messy fringes of our experiments and data; they may not change our conclusions but they should reduce our overconfidence in those conclusions. Second, to think hard about the ways in which our conclusions may be wrong. Third, to seek diversity: diversity of views and of data-gathering methods. Once we look at the same problem from several angles, we have more chances to spot our errors.

But humans being what they are, this problem isn’t likely to go away. It’s very easy to fool ourselves at the best of times. It’s particularly easy to fool ourselves when we already think we have the answer.

‘Whether the computer reckons you’re a love match or not isn’t something that anyone should take seriously’

I’ve occasionally wondered whether the secret to love is mathematics, and I’m not the only one. Mathematics is full of perky ideas about matching or sorting that have a veneer of romantic promise. But for all their beauty and cleverness, one often feels that such ideas are a far better introduction to mathematics than they are to dating and mating.

Consider the Gale-Shapley algorithm, which dates from 1962 but won Lloyd Shapley a Nobel Memorial Prize in economics just a couple of years ago. The algorithm is a way of assigning matching pairs in a stable way. By “stable”, we mean that no two people would do better ignoring the algorithm and instead making a side-arrangement with each other. The Gale-Shapley algorithm can be used for matching students to university places, or kidney donors to kidney recipients. However, it is most famously described as a way of allocating romantic partners. It is, alas, ill suited to this task, since it skips over the possibility of homosexuality, bisexuality, polyamory or even something as simple as divorce. (1962 is on the phone . . . it wants its algorithm back.)

But if pure mathematics cannot help, surely statistics can? Internet dating promises to move us away from abstractions to the more gritty reality of data. Simply type in everything you have to offer, in great detail, and let the computer algorithm find your match. What could be simpler or more efficient?

Perhaps we should be a little cautious before buying into the hype. After all, such promises have been made before. The journalist Matt Novak has unearthed an article from 1924’s Science and Invention magazine in which the magazine’s publisher Hugo Gernsback explained that humans would soon enjoy the same scientific matchmaking approach then lavished on horses. The science included the “electrical sphygmograph” (it takes your pulse) and a “body odor test” (sniffing a hose attached to a large glass capsule that contains your beau or belle).

Then, in the 1960s, enterprising Harvard students set up “Operation Match”. It was a matchmaking service powered by a punch-card IBM computer. Despite breathless media coverage, this was no more scientific than Gernsback’s sphygmograph. According to Dan Slater’s Love in the Time of Algorithms, the men who founded Operation Match were hoping for the first pick of the women themselves.

One subscriber expressed the advantages and limitations of digital dating very well: “I approve of it as a way to meet people, although I have no faith in the questionnaire’s ability to match compatible people.”

Quite so. Operation Match was a numbers game in the crudest sense. It was an easy way to reach lots of nearby singles. There should be no pretence that the computer could actually pair up couples who were ideally suited to each other.

Perhaps we simply need more data? OkCupid, a dating site with geek appeal and a witty, naughty tone, allows you to answer thousands of questions: anything from “Do you like the taste of beer?” to “Would you ever read your partner’s email?” Users typically answer several hundred such questions, as well as indicating what answer they would hope for from a would-be date, and how important they feel the question is.

Again, media reaction has been credulous. Every now and then we hear of nerds who are living the dream, playing OkCupid’s algorithms with such virtuosity that love is theirs to command. Wired magazine introduced us to Chris McKinlay, “the math genius who hacked OkCupid”. McKinlay, we are told, downloaded a dataset containing 20,000 women’s profiles and six million questionnaire answers, optimised his own profile and unleashed an army of software bots to draw women in. He was a data-driven love-magnet.

But OkCupid’s own research suggests this is all rather futile. In one controversial experiment, it took a collection of pairs of users who were a poor match, according to the OkCupid algorithm — and then told them instead that they were highly compatible. One might expect that these not-really-compatible couples would find that their conversations quickly fizzled. In fact, they did scarcely less well than couples where the algorithm genuinely predicted a match. In short, whether the computer reckons you’re a love match or not isn’t a piece of information that anyone should take seriously.

. . .

Hannah Fry, author of The Mathematics of Love, expresses the problem neatly. The algorithm, she says, “is doing exactly what it was designed to do: deliver singles who meet your specifications. The problem here is that you don’t really know what you want.”

Quite so. The list of qualities that we might want in a partner — “fascinating, sexy, fun, handsome, hilarious” — are a poor match for the list of qualities one could share with a computer database — “likes beer, boardgames, Malcolm Gladwell and redheads”. If the computer cannot pose the right questions it is hardly likely to produce the right answers.

As for Chris McKinlay, no doubt we all wish him well. He announced his engagement to Christine Tien Wang — the 88th woman he met in person after spending months in the middle of a perfect dating storm. His experience suggests that just as with Operation Match, the matching process is nonsense and the secret to finding love is to date a lot of people.

‘If Starbucks opens a café just round the corner from another Starbucks, is that really about selling more coffee?’

“New Starbucks Opens in Restroom of Existing Starbucks”, announced The Onion, satirically, in 1998. It was a glimpse of the future: there were fewer than 2,000 Starbucks outlets back then and there are more than 21,000 now. They are also highly concentrated in some places. Seoul has nearly 300 Starbucks cafés, London has about 200 — a quarter of all the Starbucks outlets in the UK — and midtown Manhattan alone has 100. It raises the question: how many Starbucks shopfronts are too many?

Such concerns predate the latte boom. In the late 1970s, Douglas Adams (also satirically) posited the Shoe Event Horizon. This is the point at which so much of the retail landscape is given over to shoe shops that utter economic collapse is inevitable.

And in 1972, the US Federal Trade Commission issued an entirely non-satirical complaint against the leading manufacturers of breakfast cereal, alleging that they were behaving anti-competitively by packing the shelves with frivolous variations on the basic cereals. That case dragged on for years before eventually being closed down by congressional action.

The intuition behind these complaints is straightforward. If Starbucks opens a café just round the corner — or in some cases, across the road — from another Starbucks, could that really be about selling more coffee, or is it about creating a retail landscape so caffeinated that no rival could survive? Similarly, the arrival on the supermarket shelves of Cinnamon Burst Cheerios might seem reasonable enough, were they not already laden with Apple Cinnamon Cheerios and Cheerios Protein Cinnamon Almond and 12 other variants on the Cheerios brand.

Conceptually, there is little difference between having outlets that are physically close together and having products that differ only in subtle ways. But it is hard to be sure exactly why a company is packing its offering so densely, at the risk of cannibalising its own sales.

A crush of products or outlets may be because apparently similar offerings reflect differences that matter to consumers. I do not much care whether I am eating Corn Flakes or Shreddies — the overall effect seems much the same to me — but others may care very much indeed. It might well be that in midtown Manhattan, few people will bother walking an extra block to get coffee, so if Starbucks wants customers it needs to be on every corner.

But an alternative explanation is that large companies deliberately open too many stores, or launch too many products, because they wish to pre-empt competitors. Firms could always slash prices instead to keep the competition away but that may not be quite as effective — a competitor might reasonably expect any price war to be temporary. It is less easy to un-launch a new product or shut down a brand-new outlet. A saturated market is likely to stay saturated for a while, then, and that should make proliferation a more credible and effective deterrent than low prices.

A recent paper by two economists from Yale, Mitsuru Igami and Nathan Yang, studies this question in the market for fast-food burgers. Igami and Yang used old telephone directories to track the expansion of the big burger chains into local markets across Canada from 1970 to 2005. After performing some fancy analysis, they concluded that big burger chains did seem to be trying to pre-empt competition. If Igami and Yang’s model is to be believed, McDonald’s was opening more outlets, more quickly than would otherwise have been profitable.

It is the consumer who must ultimately pay for these densely packed outlets and products. But perhaps the price is worthwhile. The econometrician Jerry Hausman once attempted to measure the value to consumers of Apple Cinnamon Cheerios. He concluded that it was tens of millions of dollars a year — not much in the context of an economy of $17tn a year, but not nothing either. Perhaps competitors were shut out of the market by Apple Cinnamon Cheerios but that doesn’t mean that consumers didn’t value them.

. . .

It may be helpful to consider what life would be like if every café, cereal brand or fast-food joint were owned by a separate company. Steven Salop, an economist at Georgetown University, produced an elegant economic analysis of this scenario in 1979. He found that even a market full of independents will seem a little too crowded. This is because firms will keep showing up and looking for customers until there is not enough demand to cover their costs. The last entrepreneur to enter is the one that just breaks even, scraping together enough customers to pay for the cost of setting up the business. She is indifferent to whether she is in business or doing something else entirely. However, every other entrepreneur in the crowded market is wishing that she had stayed away.

Whether the products are shoes or cereal, lattes or cheeseburgers, markets will often seem wastefully crowded. That perception is largely an illusion, but not entirely. In big city markets, there really are too many cereals, too many cafés and too many fast-food restaurants. But even if they were all mom-and-pop independents, that might still be true.

The chances of winning the UK’s National Lottery are absurdly low — almost 14 million to one against. When you next read that somebody has won the jackpot, should you conclude that he tampered with the draw? Surely not. Yet this line of obviously fallacious reasoning has led to so many shaky convictions that it has acquired a forensic nickname: “the prosecutor’s fallacy”.

Consider the awful case of Sally Clark. After her two sons each died in infancy, she was accused of their murder. The jury was told by an expert witness that the chance of both children in the same family dying of natural causes was 73 million to one against. That number may have weighed heavily on the jury when it convicted Clark in 1999.

As the Royal Statistical Society pointed out after the conviction, a tragic coincidence may well be far more likely than that. The figure of 73 million to one assumes that cot deaths are independent events. Since siblings share genes, and bedrooms too, it is quite possible that both children may be at risk of death for the same (unknown) reason.

A second issue is that probabilities may be sliced up in all sorts of ways. Clark’s sons were said to be at lower risk of cot death because she was a middle-class non-smoker; this factor went into the 73-million-to-one calculation. But they were at higher risk because they were male, and this factor was omitted. Which factors should be included and which should be left out?

The most fundamental error would be to conclude that if the chance of two cot deaths in one household is 73 million to one against, then the probability of Clark’s innocence was also 73 million to one against. The same reasoning could jail every National Lottery winner for fraud.

Lottery wins are rare but they happen, because lots of people play the lottery. Lots of people have babies too, which means that unusual, awful things will sometimes happen to those babies. The court’s job is to weigh up the competing explanations, rather than musing in isolation that one explanation is unlikely. Clark served three years for murder before eventually being acquitted on appeal; she drank herself to death at the age of 42.

Given this dreadful case, one might hope that the legal system would school itself on solid statistical reasoning. Not all judges seem to agree: in 2010, the UK Court of Appeal ruled against the use of Bayes’ Theorem as a tool for evaluating how to put together a collage of evidence.

As an example of Bayes’ Theorem, consider a local man who is stopped at random because he is wearing a distinctive hat beloved of the neighbourhood gang of drug dealers. Ninety-eight per cent of the gang wear the hat but only 5 per cent of the local population do. Only one in 1,000 locals is in the gang. Given only this information, how likely is the man to be a member of the gang? The answer is about 2 per cent. If you randomly stop 1,000 people, you would (on average) stop one gang member and 50 hat-wearing innocents.

We should ask some searching questions about the numbers in my example. Who says that 5 per cent of the local population wear the special hat? What does it really mean to say that the man was stopped “at random”, and do we believe that? The Court of Appeal may have felt it was spurious to put numbers on inherently imprecise judgments; numbers can be deceptive, after all. But the cure for “bad statistics” isn’t “no statistics” — it’s using statistical tools properly.

Professor Colin Aitken, the Royal Statistical Society’s lead man on statistics and the law, comments that Bayes’ Theorem “is just a statement of logic. It’s irrefutable.” It makes as much sense to forbid it as it does to forbid arithmetic.

. . .

These statistical missteps aren’t a uniquely British problem. Lucia de Berk, a paediatric nurse, was thought to be the most prolific serial killer in the history of the Netherlands after a cluster of deaths occurred while she was on duty. The court was told that the chance this was a coincidence was 342 million to one against. That’s wrong: statistically, there seems to be nothing conclusive at all about this cluster. (The death toll at the unit in question was actually higher before de Berk started working there.)

De Berk was eventually cleared on appeal after six years behind bars; Richard Gill, a British statistician based in the Netherlands, took a prominent role in the campaign for her release. Professor Gill has now turned his attention to the case of Ben Geen, a British nurse currently serving a 30-year sentence for murdering patients in Banbury, Oxfordshire. In his view, Geen’s case is a “carbon copy” of the de Berk one.

Of course, it is the controversial cases that grab everyone’s attention, so it is difficult to know whether statistical blunders in the courtroom are commonplace or rare, and whether they are decisive or merely part of the cut and thrust of legal argument. But I have some confidence in the following statement: a little bit of statistical education for the legal profession would go a long way.

‘The idea that we can somehow measure “the thing that matters most” is quite absurd’

As he appeals to the British public to vote him in as prime minister, the leader of the opposition proposes collecting new data to provide a better picture of how the country is doing. “Wellbeing can’t be measured by money or traded in markets,” he says. He adds, “We measure all kinds of things but the only thing we don’t measure is the thing that matters most.”

All of the preceding paragraph is true, except for one detail: the first quotation is from David Cameron, then leader of the opposition, in 2006. The second is from Ed Miliband, the current leader of the opposition, a couple of weeks ago. Both men are united, it seems, by a feeling that the most familiar economic measuring stick, GDP (Gross Domestic Product), just isn’t up to the job. Cameron wanted to gather data on wellbeing or happiness; Miliband wants a “cost of living” index. Few reasonable people can object to gathering timely and authoritative economic and social statistics, yet Miliband and Cameron have managed the impressive feat of being cynical and naive at the same time.

The cynical motives in both cases are plain enough — as were, for example, Nicolas Sarkozy’s when, as French president, he commissioned some alternative economic measures that just happened to be more flattering to France. As the leader of a party with a reputation for liking free markets and low taxes, Cameron wanted to soften his image and suggest a broader, more caring perspective. Miliband is trying to replace a government that is presiding over a sudden uptick in GDP, so naturally he wishes to point the spotlight somewhere else.

The naivety requires more statistical digging to uncover, and it’s in three parts. The first point is that many of these data already exist. The Office for National Statistics asks questions about wellbeing as part of the Labour Force Survey. The ONS also publishes regular data on inflation, while wage data are in the Annual Survey of Hours and Earnings. Neither Cameron nor Miliband was really asking the statisticians at the ONS to do something new, just to do it more often or in more detail.

The second point is that no mainstream politician has ever regarded GDP (or its cousin Gross National Product) as the only worthwhile policy objective, although we are often invited to draw that conclusion. Robert Kennedy’s famous complaint that GNP counts “napalm” and “nuclear warheads” but not “the health of our children” or “the strength of our marriages” was wonderful rhetoric — but surely nobody believes that if only the statisticians had collected different data, divorce would be prevented and the Vietnam war would never have happened.

An acerbic comment in Nature last year complained that, “Despite the destruction wrought by the Deepwater Horizon oil spill in 2010 and Hurricane Sandy in 2012, both events boosted US GDP because they stimulated rebuilding.” But this is only a problem if the Deepwater Horizon spill was in some way caused by the collection of GDP data.

If politicians truly sought to maximise GDP they would immediately abolish all planning restrictions, all barriers to immigration and a good chunk of the welfare state. These ideas are political suicide, which proves that GDP is not the sole objective of public policy — it’s just a way to try to measure the size of the economy.

The deepest piece of naivety is the idea that — in Ed Miliband’s words — we can measure the one single “thing that matters most”. ONS data on median wages are a case in point. According to one measure, the median wage for people in full-time employment rose just 0.1 per cent in the past tax year — well below the rate of inflation. According to another way of calculating exactly the same number, median wages rose by 4.1 per cent, well above the rate of inflation. (The median is the wage earned by someone slap in the middle of the sample.)

How can that be? The lower measure is the median for the entire sample. The higher measure looks at the median wage of people who’ve been in the same job for the entire year — the vast majority. The two numbers would differ if — for example — some high-income people retired and some low-income people joined the labour force (school-leavers? immigrants?). It’s possible for most people to enjoy a decent pay rise while median wages stagnate, and that may be what is happening now. One rather narrow question — “how are things going for people in full-time employment in the middle of the income distribution?” — turns out to have two very different answers. Each one is perfectly justifiable.

We haven’t even got into questions of part-timers, the self-employed, the poorest, the richest, pensioners or benefit recipients. The idea that we can somehow measure “the thing that matters most” is quite absurd.

It’s the duty of our official statisticians to provide a range of timely and objective statistics that will lead to better decisions. That is why so many different types of data must be gathered, analysed and published. It is a hard job, which is why the ONS has better things to do than help our schoolboy politicians score points off each other.

‘Every time we say yes to a request, we are also saying no to anything else we might accomplish with the time’

Every year I seem to have the same resolution: say “no” more often. Despite my black belt in economics-fu, it’s an endless challenge. But economics does tell us a little about why “no” is such a difficult word, why it’s so important — and how to become better at saying it.

Let’s start with why it’s hard to say “no”. One reason is something we economists, with our love of simple, intuitive language, call “hyperbolic discounting”. What this means is that the present moment is exaggerated in our thoughts. When somebody asks, “Will you volunteer to be school governor?” it is momentarily uncomfortable to refuse, even if it will save much more trouble later. To say “yes” is to warm ourselves in a brief glow of immediate gratitude, heedless of the later cost.

A psychological tactic to get around this problem is to try to feel the pain of “yes” immediately, rather than at some point to be specified later. If only we could feel instantly and viscerally our eventual annoyance at having to keep our promises, we might make fewer foolish promises in the first place.

One trick is to ask, “If I had to do this today, would I agree to it?” It’s not a bad rule of thumb, since any future commitment, no matter how far away it might be, will eventually become an imminent problem.

Here’s a more extreme version of the same principle. Adopt a rule that no new task can be deferred: if accepted, it must be the new priority. Last come, first served. The immediate consequence is that no project may be taken on unless it’s worth dropping everything to work on it.

This is, of course, absurd. Yet there is a bit of mad genius in it, if I do say so myself. Anyone who sticks to the “last come, first served” rule will find their task list bracingly brief and focused.

There is a far broader economic principle at work in the judicious use of the word “no”. It’s the idea that everything has an opportunity cost. The opportunity cost of anything is whatever you had to give up to get it. Opportunity cost is one of those concepts in economics that seem simple but confuse everyone, including trained economists.

Consider the following puzzle, a variant of which was set by Paul J Ferraro and Laura O Taylor to economists at a major academic conference back in 2005. Imagine that you have a free ticket (which you cannot resell) to see Radiohead performing. But, by a staggering coincidence, you could also go to see Lady Gaga — there are tickets on sale for £40. You’d be willing to pay £50 to see Lady Gaga on any given night, and her concert is the best alternative to seeing Radiohead. Assume there are no other costs of seeing either gig. What is the opportunity cost of seeing Radiohead? (a) £0, (b) £10, (c) £40 or (d) £50.

If you’re not sure of your answer, never fear: the correct answer (below), was also the one least favoured by the economists.

However dizzying the idea of opportunity cost may be, it’s something we must wrap our heads around. Will I write a book review? Will I chair a panel discussion on a topic of interest? Will I give a talk to some students? In isolation, these are perfectly reasonable requests. But viewing them in isolation is a mistake: it is only when viewed through the lens of opportunity cost that the stakes become clearer.

Will I write a book review and thus not write a chapter of my own book? Will I give a talk to some students, and therefore not read a bedtime story to my son? Will I participate in the panel discussion instead of having a conversation over dinner with my wife?

The insight here is that every time we say “yes” to a request, we are also saying “no” to anything else we might accomplish with the time. It pays to take a moment to think about what those things might be.

Saying “no” is still awkward and takes some determination. Nobody wants to turn down requests for help. But there is one final trick that those of us with family commitments can try. All those lessons about opportunity cost have taught me that every “no” to a request from an acquaintance is also a “yes” to my family. Yes, I will be home for bedtime. Yes, I will switch off my computer at the weekend.

And so from time to time, as I compose my apologetic “sorry, no”, I type my wife’s email address in the “bcc” field. The awkward email to the stranger is also a tiny little love letter to her.

Answer: Going to see Lady Gaga would cost £40 but you’re willing to pay £50 any time to see her; therefore the net benefit of seeing Gaga is £10. If you use your free Radiohead ticket instead, you’re giving up that benefit, so the opportunity cost of seeing Radiohead is £10.

‘Travelling 28 miles on a motorbike is four micromorts; cycling the same distance is just over one micromort’

The Rand Corporation was established in 1948 as an independent research arm of the US Air Force, itself newly independent and in its pomp as the wielder of the US nuclear arsenal. Rand’s early years were spent wrestling with the mathematics of Armageddon, and it has long struggled to shake off its reputation as the inspiration for Dr Strangelove.

Yet Rand’s most controversial research topic was its very first study — and its crime was to offend not the public but the top brass at the Air Force. Edwin Paxson, one of its top mathematicians, had been asked by the Air Force to think about the problem of an optimal first strike against the Soviet Union. How could the United States annihilate the Soviet Union for the smallest possible expenditure?

Paxson’s research was technically impressive, using cutting-edge analytical techniques. (The project is described in histories by David Jardini and by Fred Kaplan, and in a new article in the Journal of Economic Perspectives by Spencer Banzhaf.) His conclusion, published in 1950, was that rather than commissioning expensive turbojet bombers, the US should build large numbers of cheap propeller aircraft, most of which would carry no nuclear payload and would be little more than decoys. Not knowing which planes held atomic weapons, the Soviet defences would be overwhelmed by sheer numbers.

This conclusion infuriated the Air Force. No doubt this was partly because they viewed old-fashioned propeller aircraft as beneath their dignity. But the key offence was this: Paxson’s cost-benefit analysis gave no weight to the lives of air crew. Ten thousand pilots could be wiped out and it would make no difference to Paxson’s arithmetic. Under fire from senior officers, who had been wartime pilots themselves, Rand quickly adopted a more humble tone. It also diversified its funding by researching non-military topics.

Yet Paxson’s omission is understandable. A sensible strategist must weigh the costs and benefits of different tactics — but once one accepts the need for value for money in military strategy, what monetary value can we put on human life?

One possible approach to the problem is to value people according to some economic proxy — for example, the Air Force might value the cost of training new pilots. Courts have assigned damages after fatal accidents by looking at the economic output the dead person would otherwise have produced. But this suggests that the life of a retired person has no value. It captures the loss of livelihood, not the loss of life.

In the 1960s, a new approach emerged, most famously in Thomas Schelling’s 1968 essay “The Life You Save May Be Your Own”. Schelling, who much later won the Nobel Memorial Prize in Economic Sciences, had spent some productive time working at Rand. His student Jack Carlson was a former Air Force pilot. Carlson and Schelling found a way to finesse the treacherous question. As Schelling wrote: “It is not the worth of human life that I shall discuss but of ‘life-saving’, of preventing death. And it is not a particular death, but a statistical death.”

Rather than asking “What is the value of human life?” Schelling and Carlson asked what we are willing to pay to reduce the risk of premature death by spending money on road safety or hospitals. The value of a life was replaced with the value of a statistical life.

There is good sense in this bait-and-switch. The life of a named individual defies monetary valuation. It is special. Yet the prospect of spending money to widen and straighten a road and therefore fractionally reduce the chance that any one of thousands of road users will die — that feels like a more legitimate field for economic exploration.

For those who have not read Schelling’s elegant essay, simply inserting a qualifier into the phrase “the value of a [statistical] life” will not persuade. This presents a serious public-relations problem. From time to time it emerges that government bureaucrats have been valuing human life — outrageous! (The going rate for an individual life in the US is about $7m.)

As Trudy Ann Cameron, a professor of economics at the University of Oregon, comments, it would be helpful for economists to be able to report their research on the benefits of environmental or health policies “in a way that neither confuses nor offends non-economists”.

Here’s a possible solution: use microlives. A microlife is one millionth of an adult lifespan — about half an hour — and a micromort is a one-in-a-million chance of dying.

Sir David Spiegelhalter, my favourite risk communication expert, reckons that going under general anaesthetic is 10 micromorts. Travelling 28 miles on a motorbike is four micromorts; cycling the same distance is just over one micromort. The National Health Service in the UK uses analysis that prices a microlife at around £1.70; the UK Department for Transport will spend £1.60 to prevent a micromort. In a world where life-and-death trade-offs must be made, and should be faced squarely, this is a less horrible way to think about it all. A human life is a special thing; a microlife, not so much.

As Ronald Howard, the decision analysis expert who invented the micromort, put it back in 1984: “Although this change is cosmetic only, we should remember the size of the cosmetic industry.”

Status quo bias means that most of your stuff stays because you can’t think of a good reason to get rid of it

Now that Christmas is a brandy-soaked memory, there comes the difficult business of packing away all the gifts that haven’t been broken or eaten. Double-stack the books on the bookshelf, squeeze the woolly sweater into the sock drawer and don’t even think about trying to keep the toys tidy.

Before you blame the decadence of western civilisation for the difficulty of this seasonal clutter, note that the boom in consumer spending each December isn’t new. According to Joel Waldfogel’s brief yet comprehensive book Scroogenomics, Americans were happily splurging at Christmas three or four generations ago with much the same vigour as they do today, relative to the size of the US economy. Nor are Americans exceptional in the lavishness of their Christmas celebrations: Waldfogel reveals that many European countries enjoy an even greater blowout.

No, the trouble with all this clutter, it seems to me, is simple economics. We can afford to buy more and more Christmassy stuff — clothes in particular have been getting cheaper for many years — but the one thing that isn’t getting any cheaper is room to put all the extra stuff in. This is true for most people and it is particularly true for FT readers, who are more likely than most to live in places — New York, London, Hong Kong — where the price of a home can make almost anything look cheap in comparison.

I used to think I knew the answer to this problem: cleverly designed storage space. I am no longer so convinced. Elegantly organised cupboards simply postpone the day of reckoning. The house looks neat for a while but eventually the sheer volume of possessions can overwhelm any storage solution.

Perhaps it’s time for a new approach, and the book that’s been rocking my world for the past few weeks is Marie Kondo’s The Life-Changing Magic of Tidying. If you follow Kondo’s ideas faithfully you’re likely to be driving three-quarters of your possessions to landfill, at which point most of your storage problems should evaporate. The Harford family have all succumbed to the Marie Kondo bug in a big way and are suddenly seeing areas of the floor in our house that we had quite forgotten existed.

Kondo espouses some strange ideas. She unpacks her handbag and tidies away the contents every evening when she returns home. She firmly believes that socks need rest. She advocates saying “thank you” to possessions that are about to be discarded.

Yet despite all this oddness, what really struck me is that Kondo is an intuitive economist. I realised that I had been committing some cognitive blunders, enough to embarrass any self-respecting economist. These errors explained why my house was so full of possessions.

The first mistake was simple status quo bias — a tendency to let things stay the way they are. When you’re trying to clear stuff out of the house, it’s natural to think about whether to throw something away. Perhaps that’s the wrong question, because it places too high a barrier on disposal. Status quo bias means that most of your stuff stays because you can’t think of a good reason to get rid of it.

Kondo turns things around. For her, the status quo is that every item you own will be thrown away unless you can think of a compelling reason why it should stay. This mental reversal turns status quo bias, paradoxically, into a force for change.

My second error was a failure to appreciate the logic of diminishing returns. The first pair of trousers is essential; the second is enormously useful. It is not at all clear why anyone would want a 10th or 11th pair. It’s good to have a saucepan but the fifth saucepan will rarely be used. I love books but I already own more than I will be able to read for the rest of my life, so some of them can surely go.

The trick to appreciating diminishing returns is to gather all the similar stuff together at once. Once every single book I owned was sitting in a colossal pile on my living-room floor, the absurdity of retaining them all became far easier to appreciate.

. . .

A third mistake was not fully appreciating the opportunity cost of possessions. There’s a financial cost in paying for a storage locker or buying a larger house or simply buying more bookshelves. But there’s also the cost of being unable to appreciate what you have because it’s stuck at the bottom of a crate underneath a bunch of other things you have.

All this may seem strange talk from an economist, because economics is often associated with a kind of crass materialism. The field no doubt has flaws but materialism isn’t one of them. If anything, the blind spot in classical economics is that the last word on what consumers value is what consumers choose.

Behavioural economics, famously, has a different view — it says that we do make systematic mistakes. But until reading Kondo’s book, I didn’t realise that in every overstuffed bookshelf and cluttered cupboard those mistakes were manifesting themselves.

There is a vast discrepancy between how we see the world when giving gifts and when receiving them

The Harford girls have given Father Christmas two very different challenges this year. Miss Harford Senior typed a charming yet professional letter, illustrated with clip art, specifying a number of expensive gifts that would be greatly appreciated. Miss Harford Junior hand-wrote a short note saying that she had tried to be good this year and would like a surprise.

The girls raise two questions. Are surprise gifts better than something specifically requested on a wish list? Are expensive gifts a good way to express affection?

Father Christmas might seek guidance from a set of studies conducted by Gabrielle Adams and Francis Flynn of Stanford, and Harvard’s Francesca Gino.

Gino and Flynn surveyed married people, asking some to reflect on wedding gifts they had received, and others to think about wedding gifts they had given. Gift givers assumed that gifts chosen spontaneously would be just as welcome as those chosen from a wedding registry. Recipients felt otherwise: they preferred the gifts that had been on the wedding list. Such lists seem charmless but they work.

Gino and Flynn found similar results from a survey about birthday presents: again, givers thought that gifts they’d chosen themselves were more appreciated but recipients preferred the gifts that they’d specifically asked for. The lesson: you might feel that it’s awkward and unnecessary to ask what gift would be welcome but the recipient of the gift sees things differently and would prefer that you asked rather than guessed.

Gino and Flynn conducted a third study in which people created wish lists. Other participants were asked to choose an item on the list to be sent as a gift; a third group were asked to peruse the wish list but then to choose some other present of equivalent value. It’s not surprising to discover that recipients preferred the items from their wish list — but what’s remarkable is that they felt the wishlist gifts were more “personal” and “thoughtful”. We think that picking an item from a wish list is lazy and impersonal but the person receiving that item doesn’t see it that way at all.

For good measure, a fourth study by Gino and Flynn found there was one thing people appreciated even more than an item from their own wish lists: money.

There’s more. Adams and Flynn surveyed newly engaged couples about engagement rings. The givers assumed that more expensive rings were more appreciated. The recipients felt differently. A similar result came from asking people to think about a particular birthday present they had received or given: recipients were just as happy with inexpensive gifts, to the surprise of givers.

In short, there is a vast discrepancy between how we see the world when giving gifts and when receiving them. The gift giver imagines that the ideal present is expensive and surprising; the recipient doesn’t care about the money and would rather have a present they’d already selected. We should spend less than we think, and we should ask more questions before we buy.

All of this makes good sense in light of “The Deadweight Loss of Christmas”, a scholarly piece of research conducted by Joel Waldfogel and published in a leading academic journal, the American Economic Review. It celebrates its 21st birthday this month. (Congratulations, Joel.)

Waldfogel’s work on Christmas is well known to readers of this column but here is a quick summary for those who have forgotten. After surveying his students about gifts they had received over the holiday season, he found that most gifts were poorly chosen relative to what the students would have selected themselves. Gifts from friends and lovers tended to be better chosen than gifts from elderly relatives but, on average, the waste attributable to poorly chosen seasonal gifts was between 15 and 20 per cent of the purchase price of the gift — that’s well over $10bn wasted in the US alone every Christmas. This is a vast squandering of time, energy and valuable raw materials.

The usual response to this is that economists have, yet again, failed to appreciate the true meaning of Christmas. But to me this simply suggests that economists have managed to acquire a toxic brand in matters of human relations.

Were a priest to counsel against materialism at Christmas, nobody would accuse him or her of missing the point; the same message from an economist seems foolish and emotionally stunted.

Coupled with the findings from Adams, Flynn and Gino, the conclusion is plain: there is no need to stop buying Christmas presents but we should spend less and pay more attention to what the recipients might actually want.

So what should Father Christmas conclude when faced with my daughters’ letters? Miss Harford Senior is wise to specify exactly what she wants and Father Christmas should take heed.

Miss Harford Junior is taking a risk asking for a surprise — but at least Father Christmas knows that the last thing he should do to compensate for his ignorance is desperately spend more money.

‘Something about the culture of UK schools is nudging young women away from economics’

It’s no secret that women have long faced an uphill battle both to achieve success and be recognised for that success. The Nobel Prizes tell the story as well as anything: 860 people have been awarded prizes (including the unofficial Nobel Memorial Prize in economics) but only 5 per cent of them were women. The imbalance is worse still in stereotypically male subjects: only six Nobels for physics or chemistry have been awarded to women, fewer than 2 per cent of the total. Marie Curie won two of them; her daughter Irène won another.

Economics is another subject with a masculine reputation. It does not seem to be a happier hunting ground. The economics prize in memory of Alfred Nobel was launched in 1969 but it wasn’t until 2009 that Elinor Ostrom became the only woman so far to win it. “I won’t be the last,” was her characteristically practical comment.

Ostrom won the Nobel in economics despite not being an economist — her application to study for a PhD was turned away by UCLA’s economics department because she didn’t have the maths. “I had been advised as a girl against taking any courses beyond algebra and geometry in high school,” she commented. This particular piece of sexism ultimately worked in her favour: she became a political scientist instead and ended up approaching economic problems from a fresh perspective.

Curie faced a more immediate form of discrimination: in 1903 the Nobel physics committee planned to award the prize to her husband Pierre and to Henri Becquerel, overlooking Marie’s central role in studying radiation. Pierre insisted that his wife should receive the credit that she deserved. Not every husband of a brilliant wife has been quite so enlightened.

The two stories show the range of possibilities for discrimination to occur. Ostrom’s career path was shaped by negative stereotypes more than 60 years before she eventually won her prize; Curie nearly had the prize snatched away at the moment of triumph.

These are old wounds, and we have made a great deal of progress since then. But gender imbalances remain. In the US, the National Science Foundation’s survey of earned doctorates is not a bad place to look for the state of play. In 2012 women earned 46 per cent of all doctorates, up from 32 per cent three decades earlier. No great cause for alarm there. And women heavily outnumber men in social sciences such as psychology, sociology and anthropology.

Yet economics is a different beast: more than two-thirds of economics doctorates are awarded to men. (There is a similar story to tell in physics, chemistry, computing and engineering.) Since nobody under the age of 50 has won the Nobel Prize in economics, one can expect this imbalance in economics PhDs today to ripple through the upper echelons of the profession for many years to come.

There are also hopeful signs. The proportion of economics doctorates earned by women has been growing. The John Bates Clark medal, a prestigious award for economists under the age of 40, was exclusively male until Susan Athey won in 2007, but two other women have won the award since then. That is a sharp shift.

Is the lesson that all we need to do to attract more women to economics is wait? That is doubtful. In the UK, the proportion of undergraduate economists who are women is 27 per cent and falling. This isn’t a problem that will fix itself. So what can be done? The answer to that question depends on where we think the source of the imbalance lies — are we facing Marie Curie’s problem, or Lin Ostrom’s, or something else?

The school environment seems as significant today as it was for Ostrom. A recent study by Mirco Tonin and Jackie Wahba of the University of Southampton examines enrolment in undergraduate economics degrees in the UK. The gender imbalance in successful applicants is much more pronounced among UK applicants than those applying to UK universities from overseas. That suggests that something about the culture of UK schools is nudging young women away from economics.

. . .

That something may well be mathematics. This subject, a vital foundation for economics, is studied by more boys than girls at A-Level. Such a gender gap in advanced high-school mathematics disappeared in the United States 20 years ago.

As for women who already have their PhDs and are looking for careers in academia, the situation in the US is not entirely encouraging. A recent detailed study by a team of economists and psychologists (Stephen Ceci, Donna Ginther, Shulamit Kahn and Wendy Williams) looked at women in US academic sciences and concluded that while “gender discrimination was an important cause of women’s under-representation in scientific academic careers, this claim has continued to be invoked after it has ceased being a valid cause of women’s under-representation”. The playing field, they suggest, is much more level than it once was; a modern Marie Curie wouldn’t need her husband to fight her corner.

But Ceci and colleagues note an exception — one maths-intensive subject at which well-qualified and productive women somehow find it hard to win academic promotions. It’s economics. For some reason, the dismal science remains heavy with the scent of testosterone.
Written for and first published at ft.com.